Re: Is one-to-one mapping valid for comparing infinite-sized sets?

Salviati schrieb:
However, I am convinced his own
answer was unable to resolve the challenge by Buridan's donkey.

I've told you this before: there's is an unbroken chain of theorems and
their proofs, that lead to real numbers.

Assuming that real numbers are an archimedian ordered field,
1. you can prove, that Dedekind cuts and the LUB property are equivalent.
2. then you prove, that every bounded sequence converges to its LUB.
3. next, you can prove, that interval nesting works, i.e. that you get a
real number from it.
4. and then you can prove, that every decimal expansion is a real number,
and vice versa, that every real number has a decimal expansion.
5. further you can prove, that IR is complete, i.e. that the limit of every
convergent cauchy sequence actually is a real number.

However, his sentence
"The natural numbers were made by God" shows that he could not offer an
alternative to Cantor

Until today nobody has ever offered something better for IR than the above.
And you and the other cranks with their ridiculous philosphical pretexts
won't either - where the latter is, I believe, a clear consequence of the
former.

And: if I were Buridan's donkey,
I'd flip a coin, eat one haystack, and the other the next day ...

Viele Grüße
Klaus
.

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